Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

Computational Social Networks

Table 2 Results on modularity optimization

Graph	Size	[25]	EO [26]	GSO^a	EvoGSO^b
Karate	34	0.3810/2	\({0.4188}\)*/4	0.4198/4	0.4198/4
Jazz	198	0.4379/4	0.4452/5	\({0.4451}\)*/4	\({0.4451}\)*/4
C.elegans	453	0.4001/10	\({0.4342}\)*/12	0.4304/8	0.4418/11
E-mail	1133	0.4796/13	0.5738/15	0.5275/8	\({0.5655}\)*/15

We report the maximum modularity value Q and the corresponding number of communities Ncoms in the form of (Q/Ncoms)
The best and the second best results are denoted in italic and asterisk, respectively
^aConfiguration: batch size = 256, initial \(\tau\) = 0.5, final \(\tau\) = 0.1, learning rate = 0.01, instance = 10
^bConfiguration: batch size = 256, initial \(\tau\) = 0.5, final \(\tau\) = 0.1, learning rate = 0.01, instance = 10, cycle \(T_1\) = 100, cycle \(T_2\) = 5000, substitution ratio 1/u = 1/8, mutation rate m = 0.001, and elite ratio = 0.0625